Music Fundamentals 2: Rhythm and Meter

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. Duration: Note Lengths in Written Music

. Duration: Rest Length

. Dots, Ties, and Borrowed Divisions

. Rhythm

. Time Signature

. Introduction to Subdivisions in Simple Meters
. Simple and Compound Time Signatures

. Meter in Music

. Introduction to Subdivisions in Compound Meters
. Pickup Notes and Measures

. Tempo

Duration: Note Lengths in Written Music
In standard music notation, the duration (time length) of a particular note is
defined by how long it lasts compared to a whole note.

The Shape of a Note

In standard notation, a single musical sound is written as a note. The two
most important things a written piece of music needs to tell you about a
note are its pitch - how high or low it is - and its duration - how long it
lasts.

To find out the pitch of a written note, you look at the clef and the key
signature, then see what line or space the note is on. The higher a note sits
on the staff, the higher it sounds. To find out the duration of the written
note, you look at the tempo and the time signature and then see what the
note looks like.

The Parts of a Note

dot

flag

head —> - /
(not filled in) < ds .

~m head (filled in)

All of the parts of a written note
affect how long it lasts.

The pitch of the note depends only on what line or space the head of the
note is on. (Please see pitch , clef and key_signature for more information.)
If the note does not have a head (see [link]), that means that it does not have
one definite pitch.

Notes Without Heads

Headless notes have Notes with slashes instead of heads
definite rhythm but not are a quick way to write an entire chord
definite pitch. and may be easier for some instrumentalists

(such as guitarists) to read.

If a note does not have head, it does not have one
definite pitch. Such a note may be a pitchless
sound, like a drum beat or a hand clap, or it may be
an entire chord rather than a single note.

The head of the note may be filled in (black), or not. The note may also
have (or not) a stem, one or more flags, beams connecting it to other notes,
or one or more dots following the head of the note. All of these things affect
how much time the note is given in the music.

Note:A dot that is someplace other than next to the head of the note does
not affect the rhythm. Other dots are articulation marks. They may affect
the actual length of the note (the amount of time it sounds), but do not
affect the amount of time it must be given. (The extra time when the note
could be sounding, but isn't, becomes an unwritten rest.) If this is
confusing, please see the explanation in articulation.

The Length of a Note

Most Common Note Lengths

OQ Whole note J Quarter note a Sixteenth note

; Half Note ) Eighth note S Thirty-second note

The simplest-looking note, with no stems or flags, is a whole note. All
other note lengths are defined by how long they last compared to a whole
note. A note that lasts half as long as a whole note is a half note. A note
that lasts a quarter as long as a whole note is a quarter note. The pattern
continues with eighth notes, sixteenth notes, thirty-second notes, sixty-
fourth notes, and so on, each type of note being half the length of the
previous type. (There are no such thing as third notes, sixth notes, tenth
notes, etc.; see Dots, Ties, and Borrowed Divisions to find out how notes of
unusual lengths are written.)

One Two Four Eight

whole = a = — And
half quarter eighth

note notes notes notes soon

Note lengths work just like fractions in
arithmetic: two half notes or four quarter notes
last the same amount of time as one whole note.
Flags are often replaced by beams that connect
the notes into easy-to-read groups.

You may have noticed that some of the eighth notes in [link] don't have
flags; instead they have a beam connecting them to another eighth note. If
flagged notes are next to each other, their flags can be replaced by beams
that connect the notes into easy-to-read groups. The beams may connect
notes that are all in the same beat, or, in some vocal music, they may

connect notes that are sung on the same text syllable. Each note will have
the same number of beams as it would have flags.
Notes with Beams

SS SS SS

The notes connected with beams are easier
to read quickly than the flagged notes.
Notice that each note has the same number
of beams as it would have flags, even if it
is connected to a different type of note.
The notes are often (but not always)
connected so that each beamed group gets
one beat. This makes the notes easier to
read quickly.

You may have also noticed that the note lengths sound like fractions in
arithmetic. In fact they work very much like fractions: two half notes will
be equal to (last as long as) one whole note; four eighth notes will be the
same length as one half note; and so on. (For classroom activities relating
music to fractions, see Fractions, Multiples, Beats, and Measures. )

Example:

o= ad

1 whole note = 2 half notes

iJ= 0

1 half note + 2 quarter notes = 1 whole note

S\N AHS
ee@ee#eeé
4 eighth notes = 1 half note

Exercise:

Problem:

Draw the missing notes and fill in the blanks to make each side the
same duration (length of time).

CL] t+

1 whole = quarters 1 half = quarters
1 whole = eighths lThalf = 1 quarter + eighths
4sixteenths = 1 4eighths + Thalf= 1

Solution:

eeljiJJ) 4°

1whole = 4 quarters half = 2 quarters
1 whole = 8 eighths lhalf = 1quarter+ 2 eighths
4sixteenths = (1 quarter 4eighths + 1 half = 1__whole

So how long does each of these notes actually last? That depends on a
couple of things. A written note lasts for a certain amount of time measured
in beats. To find out exactly how many beats it takes, you must know the
time signature. And to find out how long a beat is, you need to know the
tempo.

Example:
Beats are slow and long
Largo —

e) K a half note is twice as long
Quarter note gets one beat as a quarter note.

But

a half note on the second staff

will be a lot shorter than

=== a half note on the first staff.
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e

f.
Al a“ Beats are fast and short

Half notes get one beat

In any particular section of a piece of music, a
half note is always twice as long as a quarter
note. But how long each note actually lasts
depends on the time signature and the tempo.

More about Stems

Whether a stem points up or down does not affect the note length at all.
There are two basic ideas that lead to the rules for stem direction. One is
that the music should be as easy as possible to read and understand. The
other is that the notes should tend to be "in the staff" as much as reasonably
possible.

Basic Stem Direction Rules

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2

Single Notes - Notes below the middle line of the staff should be stem
up. Notes on or above the middle line should be stem down.

. Notes sharing a stem (block chords) - Generally, the stem direction

will be the direction for the note that is furthest away from the middle
line of the staff

. Notes sharing a beam - Again, generally you will want to use the

stem direction of the note farthest from the center of the staff, to keep
the beam near the staff.

. Different rhythms being played at the same time by the same

player - Clarity requires that you write one rhythm with stems up and
the other stems down.

. Two parts for different performers written on the same staff - If

the parts have the same rhythm, they may be written as block chords.
If they do not, the stems for one part (the "high" part or "first" part)
will point up and the stems for the other part will point down. This rule
is especially important when the two parts cross; otherwise there is no
way for the performers to know that the "low" part should be reading
the high note at that spot.

Stem Direction

Single notes Notes ona beam

Notes in chords Separate parts

Keep stems and beams in or near the staff, but also
use stem direction to clarify rhythms and parts
when necessary.

Duration: Rest Length
In standard music notation, rests of different lengths have different shapes.

A rest stands for a silence in music. For each kind of note, there is a written
rest of the same length.
The Most Common Rests

Whole Half Quarter Eighth Sixteenth Thirty-second
Rest Rest Rest Rest Rest Rest
Exercise:
Problem:

For each note on the first line, write a rest of the same length on the
second line. The first measure is done for you.

a rs a a a rr ee ee
ae ee ee, ee ee ee ee ee ee eee eee

f= SE es ee ee ee ee ee ee ee ee ee eee ee ee ee ee ee ee
Mi a 2 re 2 ee ee 2 ee 2 2 eee)

Solution:

Rests don't necessarily mean that there is silence in the music at that point;
only that that part is silent. Often, on a staff with multiple parts, a rest must
be used as a placeholder for one of the parts, even if a single person is
playing both parts. When the rhythms are complex, this is necessary to
make the rhythm in each part clear.

When multiple simultaneous rhythms are written
on the same staff, rests may be used to clarify
individual rhythms, even if another rhythm contains
notes at that point.

The normal rule in common notation is that, for any line of music, the notes
and rests in each measure must "add up" to exactly the amount in the time
signature, no more and no less. For example, in 3/4 time, a measure can
have any combination of notes and rests that is the same length as three
quarter notes. There is only one common exception to this rule. As a
simplifying shorthand, a completely silent measure can simply have a
whole rest. In this case, "whole rest" does not necessarily mean "rest for the
same length of time as a whole note"; it means "rest for the entire measure”.

A whole rest may be used to indicate
a completely silent measure, no

matter what the actual length of the
measure will be.

Dots, Ties, and Borrowed Divisions

In written music, standard note lengths are always halves (or halves of
halves, and so on) of other note lengths. To get any other note length, dots,
ties, or borrowed divisions must be used.

A half note is half the length of a whole note; a quarter note is half the
length of a half note; an eighth note is half the length of a quarter note, and
so on. (See Duration:Note Length.) The same goes for rests. (See Duration:
Rest Length.) But what if you want a note (or rest) length that isn't half of
another note (or rest) length?

Dotted Notes

One way to get a different length is by dotting the note or rest. A dotted
note is one-and-a-half times the length of the same note without the dot. In
other words, the note keeps its original length and adds another half of that
original length because of the dot. So a dotted half note, for example, would
last as long as a half note plus a quarter note, or three quarters of a whole
note.

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The dot
acts as if
it is
adding
another
note half
the

length of
the
original
note. A
dotted
quarter
note, for
example
, would
be the
length of
a quarter
plus an
eighth,
because
an
eighth
note is
half the
length of
a quarter
note.

Exercise:

Problem:

Make groups of equal length on each side, by putting a dotted note or
rest in the box.

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A note may have more than one dot. Each dot adds half the length that the
dot before it added. For example, the first dot after a half note adds a
quarter note length; the second dot would add an eighth note length.

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When a note has
more than one dot,
each dot is worth
half of the dot
before it.

Tied Notes

A dotted half lasts as long as a half note plus a quarter note. The same
length may be written as a half note and a quarter note tied together. Tied
notes are written with a curved line connecting two notes that are on the
same line or the same space in the staff. Notes of any length may be tied
together, and more than two notes may be tied together. The sound they
stand for will be a single note that is the length of all the tied notes
added together. This is another way to make a great variety of note
lengths. Tied notes are also the only way to write a sound that starts in one
measure and ends in a different measure.

Note: Ties may look like slurs, but they are not the same; a slur connects to
notes with different pitches and is a type of articulation.

When these eight notes are played as
written, only five distinct notes are heard:
one note the length of two whole notes; then
a dotted half note; then another note the
same length as the dotted half note; then a
quarter note; then a note the same length as
a whole note plus a quarter note.

Borrowed Divisions

Dots and ties give you much freedom to write notes of varying lengths, but
so far you must build your notes from halves of other notes. If you want to
divide a note length into anything other than halves or halves of halves - if
you want to divide a beat into thirds or fifths, for example - you must write
the number of the division over the notes. These unusual subdivisions are
called borrowed divisions because they sound as if they have been
borrowed from a completely different meter. They can be difficult to
perform correctly and are avoided in music for beginners. The only one that
is commonly used is triplets, which divide a note length into equal thirds.
Some Borrowed Divisions
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Any common note length can
be divided into an unusual
number of equal-length notes
and rests, for example by
dividing a whole note into
three instead of two "half"
notes. The notes are labeled
with the appropriate number.
If there might be any question
as to which notes are
involved in the borrowed
division, a bracket is placed
above them. Triplets are by
far the most common
borrowed division.

Borrowed Duplets

a a _ a
ft A! —

f.. =e ——————— ooo
Ghee a a a a ao 2 a 2 oo on

In a compound meter,
which normally divides a
beat into three, the
borrowed division may
divide the beat into two, as
in a simple meter. You
may also see duplets in
swing music.

Notes in jazzy-sounding music that has a "swing" beat are often assumed to
be triplet rhythms, even when they look like regular divisions; for example,
two written eighth notes (or a dotted quarter-sixteenth) might sound like a
triplet quarter-eighth rhythm. In jazz and other popular music styles, a

tempo notation that says swing usually means that all rhythms should be
played as triplets. Straight means to play the rhythms as written.

Note:Some jazz musicians prefer to think of a swing rhythm as more of a
heavy accent on the second eighth, rather than as a triplet rhythm,
particularly when the tempo is fast. This distinction is not important for
students of music theory, but jazz students will want to work hard on using
both rhythm and articulation to produce a convincing "swing".

Swing Rhythms

we FD
we FD

ll ll

Jazz or blues with a
"swing" rhythm often
assumes that all divisions
are triplets. The swung
triplets may be written as
triplets, or they may
simply be written as
"straight" eighth notes or
dotted eighth-sixteenths. If
rhythms are not written as
triplets, the tempo marking
usually includes an
indication to "swing", or it
may simply be implied by
the style and genre of the
music.

Rhythm
An introduction to the basic element of music called rhythm, with some
definitions.

musical performance. They are often called the basic elements of music.
The main purpose of music theory is to describe various pieces of music in
terms of their similarities and differences in these elements, and music is
usually grouped into genres based on similarities in all or most elements.
It's useful, therefore, to be familiar with the terms commonly used to
describe each element. Because harmony is the most highly developed
aspect of Western music, music theory tends to focus almost exclusively on
melody and harmony. Music does not have to have harmony, however, and
some music doesn't even have melody. So perhaps the other three elements
can be considered the most basic components of music.

Music cannot happen without time. The placement of the sounds in time is
the rhythm of a piece of music. Because music must be heard over a period
of time, rhythm is one of the most basic elements of music. In some pieces
of music, the rhythm is simply a "placement in time" that cannot be
assigned a beat or meter, but most rhythm terms concern more familiar
types of music with a steady beat. See Meter for more on how such music is
organized, and Duration and Time Signature for more on how to read and
write rhythms. See Simple Rhythm Activities for easy ways to encourage
children to explore rhythm.

Rhythm Terms

¢ Rhythm - The term "rhythm" has more than one meaning. It can mean
the basic, repetitive pulse of the music, or a rhythmic pattern that is
repeated throughout the music (as in "feel the rhythm"). It can also
refer to the pattern in time of a single small group of notes (as in "play
this rhythm for me").

¢ Beat - Beat also has more than one meaning, but always refers to
music with a steady pulse. It may refer to the pulse itself (as in "play
this note on beat two of the measure"). On the beat or on the
downbeat refer to the moment when the pulse is strongest. Off the
beat is in between pulses, and the upbeat is exactly halfway between

pulses. Beat may also refer to a specific repetitive rhythmic pattern
that maintains the pulse (as in "it has a Latin beat"). Note that once a
strong feeling of having a beat is established, it is not necessary for
something to happen on every beat; a beat can still be "felt" even if it
is not specifically heard.

Measure or bar - Beats are grouped into measures or bars. The first
beat is usually the strongest, and in most music, most of the bars have
the same number of beats. This sets up an underlying pattern in the
pulse of the music: for example, strong-weak-strong-weak-strong-
weak, or strong-weak-weak-strong-weak-weak. (See Meter.)

Rhythm Section - The rhythm section of a band is the group of
instruments that usually provide the background rhythm and chords.
The rhythm section almost always includes a percussionist (usually on
a drum set) and a bass player (usually playing a plucked string bass of
some kind). It may also include a piano and/or other keyboard players,
more percussionists, and one or more guitar players or other strummed
or plucked strings. Vocalists, wind instruments, and bowed strings are
usually not part of the rhythm section.

Syncopation - Syncopation occurs when a strong note happens either
on a weak beat or off the beat. See Syncopation.

Time Signature

The time signature on a musical staff tells you the meter of the music by
defining both the number of beats in a measure and the type of note that
fills one beat.

In common notation, the time signature appears at the beginning of a piece
of music, right after the key signature. Unlike the key signature, which is on
every staff, the time signature will not appear again in the music unless the
meter changes. The meter of a piece is a repetitive rhythmic pulse that
underlies the music. The time signature is the symbol that tells you what
meter is being used in a piece of music and what types of note) are being

used to write it out.
Key Signature

Time Signature
Clef

The time
signature appears
at the beginning
of the piece of
music, right after
the clef symbol
and key signature.

Beats and Measures

Music happens over a period of time, so a very common way to organize
music is to divide that time into short periods of the same length, using
audible pulses called beats. Each pulse is a beat, and the regular,
predictable pulse of a piece of music is the beat. The beat is created when
the musicians do things (like hit a drum, strum a guitar, or start singing a
word) at very regular intervals. This creates an audible, predictable pulse
that helps the musicians to coordinate what they are doing so that they
sound good together. The predictability and audibility of the beat also

allows others to join in. As soon as listeners can "feel the beat," they can
clap hands, snap fingers, tap their feet, nod their heads, march, dance, or
sing along "in time" with the music (in other words, coordinated with the
musicians). Anything that happens during the audible pulse (a clap or drum
hit, for example), as well as anything that starts during a pulse (such as a
sung word, or a note on a flute or violin) is said to be on the beat. Of
course, things can happen in between the beats, too, but the timing for those
is also coordinated using the beats; for example, a note might begin at
exactly the halfway point between two beats.

Note:Not all music has beats and a time signature. In music with a free
rhythm or meter, there is no time signature, and no regular pulse to the
music; the musicians are free to play or sing a note at whatever time they
feel is best. Other pieces may have a written time signature, to help the
musicians keep track of time, but the musical events in the piece do not
give it an audible beat.

Example:

Listen to excerpts A, B, C and D. Can you clap your hands, tap your feet,
or otherwise move "to the beat"? Is there a piece in which it is easier or
harder to feel the beat?

ID. 12 Ih [>

When music is organized into beats, it makes sense to write it down that
way. In common notation, the composer assigns a particular kind of note to
be one beat long. For example, if "a quarter note gets a beat," then playing
many quarter notes in a row would mean playing a new note on every beat.

The quarter note is most likely to play this role, but any type of note can get
the "this is one beat" designation.

In most metered music, some of the beats are stronger (louder, more
powerful, more noticeable, or busier), than others, and there is a regular
pattern of stronger and weaker beats, for example, strong-weak-weak-
strong-weak-weak, or strong-weak-strong-weak. So the beats are organized
even further by grouping them into bars, or measures. (The two words
mean the same thing.) For example, for music with a beat pattern of strong-
weak-weak-strong-weak-weak, or 1-2-3-1-2-3, a measure would have three
beats in it. The time signature tells you two things: how many beats there
are in each measure, and what type of note gets a beat.

Reading the Time Signature

Top number = how many beats are in one measure

@ Bottom number = what type of note gets one beat

This time signature means that
there are three quarter notes (or
any combination of notes that
equals three quarter notes) in
every measure. A piece with
this time signature would be "in
three four time" or just "in three
four".

Exercise:
Problem:
Listen again to the music in [link]. Instead of clapping, count each
beat. Decide whether the music has 2, 3, or 4 beats per measure. In

other words, does it feel more natural to count 1-2-1-2, 1-2-3-1-2-3, or
1-2-3-4-1-2-3-4?

Solution:

e A has a very strong, quick 1-2-3 beat.

B is in a slow (easy) 2. You may feel it in a fast 4.

¢ Cis ina stately 4.

e Dis in 3, but the beat may be harder to feel than in A because the
rhythms are more complex and the performer is taking some
liberties with the tempo.

Reading Time Signatures

Most time signatures contain two numbers. The top number tells you how
many beats there are in a measure. The bottom number tells you what kind
of note gets a beat.

4 beats in a measure

- 4 quarters = twohalves = one whole = 2 quarters and four eighths = and so on

A quarter note gets one beat

In "four four" time, there are four beats in a measure
and a quarter note gets a beat. In order to keep the
meter going steadily, every measure must have a
combination of notes and rests that is equivalent to
four quarter notes.

You may have noticed that the time signature looks a little like a fraction in
arithmetic. Filling up measures feels a little like finding equivalent
fractions, too. In "four four time", for example, there are four beats in a
measure and a quarter note gets one beat. So four quarter notes would fill
up one measure. But so would any other combination of notes and rests that

equals four quarters: one whole, two halves, one half plus two quarters, a
half note and a half rest, and so on.

Example:

If the time signature is three eight, any combination of notes that adds up
to three eighths will fill a measure. Remember that a dot is worth an extra
half of the note it follows. Listen to the rhythms in [link].

A)

io ESE Ee Ee ES SS EEE SS ee
eT ER A A A

3eighths = 6sixteenths = quarter = dotted = 2eights
+1 eighth quarter + 2 sixteenths

If the time signature is three eight, a measure may be
filled with any combination of notes and rests that
adds up to three eight.

Exercise:

Problem:

Write each of the time signatures below (with a clef symbol) at the
beginning of a staff. Write at least four measures of music in each time
signature. Fill each measure with a different combination of note
lengths. Use at least one dotted note on each staff. If you need some
staff paper, you can download this PDF file.

1. Two four time
2. Three eight time
3. Six four time

Solution:

There are an enormous number of possible note combinations for any
time signature. That's one of the things that makes music interesting.

Here are some possibilities. If you are not sure that yours are correct,
check with your music instructor.

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(4a a , @ @ @ |g @ @€@ @ 4
, , es Ss

These are only a few of the many, many possible note
combinations that could be used in these time
signatures.

A few time signatures don't have to be written as numbers. Four four time is
used so much that it is often called common time, written as a bold "C".
When both fours are "cut" in half to twos, you have cut time, written as a
"C" cut by a vertical slash.

=== >

“Common time" Four four time
és (
* Cut time " = Two two time

Counting and Conducting

You may have already noticed that a measure in four four time looks the
Same as a Measure in two two. After all, in arithmetic, four quarters adds up
to the same thing as two halves. For that matter, why not call the time
signature "one one" or "eight eight"?

WWW Jib bd f

4

\ = beginning of a beal

Measures in all of these meters look the same, but
feel different. The difference is how many
downbeats there are in a measure.

Or why not write two two as two four, giving quarter notes the beat instead
of half notes? The music would look very different, but it would sound the
same, as long as you made the beats the same speed. The music in each of

the staves in [link] would sound like this.

The music in each of these staves should sound
exactly alike.

So why is one time signature chosen rather than another? The composer
will normally choose a time signature that makes the music easy to read and
also easy to count and conduct. Does the music feel like it has four beats in
every measure, or does it go by so quickly that you only have time to tap
your foot twice in a measure?

A common exception to this rule of thumb is six eight time, and the other
time signatures (for example nine eight and twelve eight) that are used to
write compound meters. A piece in six eight might have six beats in every
measure, with an eighth note getting a beat. But it is more likely that the
conductor (or a tapping foot) will give only two beats per measure, with a
dotted quarter (or three eighth notes) getting one beat. In the same way,
three eight may only have one beat per measure; nine eight, three beats per
measure; and twelve eight, four beats per measure. Why the exceptions?
Since beats normally get divided into halves and quarters, this is the easiest
way for composers to write beats that are divided into thirds.

| = beginning of a beat
Vv

In six eight time, a dotted quarter
usually gets one beat. This is the
easiest way to write beats that are
evenly divided into three rather than
two.

Introduction to Subdivisions in Simple Meters
Introduction to subdivisions in simple meters. The module introduces
divisions and subdivisions as a tool for rhythmic accuracy in music.

In general, we more accurately gauge shorter periods than longer periods of
time. For instance, the difference between the length of whole notes
performed at a quarter note = 60 and then at 66 would be difficult to
discern. However, we can easily discern the difference between sixteenth
notes performed at those speeds, four to a quarter-note beat. Our ability to
perceive smaller increments of time can help us with the larger time spans.
By accumulating many smaller time spans we can accurate measure or
perceive the larger ones.

“Subdivision” or “subdividing” refers to dividing the beat, most often
silently, into smaller units. Technically speaking divisions are note values
that divide beats (in 4/4 and 6/8 they are eighth notes) and subdivisions are
note values that further divide divisions (in 4/4 and 6/8 they are sixteenth
notes). Informally, however, most performing musicians use the term
subdivision to describe counting note values smaller than the beat. Usually
these note values are eighth or sixteenth notes. The ability to subdivide
while performing music ensures rhythmic accuracy and is an important skill
that all musicians need to develop.

Simple meters (2/4, 3/4, 4/4 etc.) generally feature subdivisions of the beat
in four parts. In the figure below please notice that the sixteenth notes form
subdivisions of all of the larger value notes:

Below is an example with subdivisions: the upper part is aligned with
sixteenth note subdivisions in the lower part:

The first step to internalizing the subdivisions is to beat out a steady pattern
of sixteenth notes while playing a melody line. For instance, while tapping
16th notes with a hand or foot try singing or saying the upper part with “ta
or “la” for each note. This may take a little bit of practice.

Try tapping out eighth notes while performing these simple patterns:

When you are able to perform the rhythms accurately with tapping, try to
then perform them accurately by internally “hearing” the taps. When I
subdivide I usually do so with internal “tapping” sounds rather than
counting “1 ee and ah, 2 ee and ah.” The internal tapping works better with
more complex rhythms or faster subdivisions.

When you have mastered the above examples with eighth notes, try
subdivisions of sixteenth notes. Here are some further examples to practice
with sixteenth note subdivisions:

IF) Sad FFA A d
Gd dd STs it STR
257] J fT) Jaf) Tid

Choosing Note Values for Subdivisions

Audio engineers speak of “sampling rates,” that is the rate at which sound
waves are digitally sampled. The higher the sampling rate, the more

accurate is the digital representation of the sound. Similarly in the
performance of music, the more subdivisions are made in each beat or each
measure, the more exacting the rhythmic performance.

Consider the following figure with notes placed rhythmically placed
spatially along the staff line:

If we add eighth note pulses we obtain:

al 2

The sixteenth notes at numbers 1 and 2 appear rhythmically accurate; at
least they are positioned so that they don’t intersect the eighth note lines.
However, if we subdivide the example with sixteenth notes (presented in
the green and blue lines) we notice that the rhythmic placement at number 2
is not accurate:

The sixteenth at number 1 coincides with the sixteenth note pulse (blue
line) but the sixteenth at number 2 clearly is not centered with the
appropriate sixteenth note pulse. The slight rhythmic sloppiness is hardly
noticeable with eight note divisions but becomes quite obvious with the
sixteenth note subdivisions.

Thus, the smaller and more frequent the rhythmic subdivisions, the more
accurately the rhythms can be scrutinized. For this reason, musicians with
the highest degree of rhythmic accuracy have the greatest mastery of very
rapid subdivisions.

The rule of thumb is to pick the smallest value of subdivision you can
internally hear when you perform.

Simple and Compound Time Signatures
Brief presentation of simple and compound time signatures.

Simple and Compound Time Signatures

Simple Time Signatures

Type Common Uncommon

Simple Duple

Simple Triple

In simple time signatures the top number represents the number of beats per
measure. The bottom number indicates the type of note equal to one beat.
The division of the beat is the lower number multiplied by 2. Thus, the
division of the beat is grouped by twos.

Example: 4-—There are 4 beats in each measure.
4—A quarter note equals one beat. Division of the beat is two eighth notes.

Compound Time Signatures

Type Common

Compound Duple
Compound Triple 9 9 9
4 8 16

Compound Quadruple 12
4

In compound time signatures the top number divided by 3 represents the
number of beats per measure. The bottom number indicates the type of note
that divides the beat. The division of the beat is grouped by threes.

Example: %—There are 3 beats per measure.
16 — Three sixteenth notes equals 1 beat.

Hearing simple and compound time signatures

Listen carefully for the pulse or beat of the music. Do you hear divisions of
two or three? A simple test is to try saying "apple" or "pineapple" to each
beat. "Apple" has two syllables and will fit simple meters. "Pineapple"--
having three syllables--naturally fits compound meters.

Protions created by Laurel A. Ewell and used with her permission.

Meter in Music

The meter of a piece of music is the repetitive arrangement of strong and
weak pulses in the rhythm. Young children can be encouraged to recognize
and classify meters even before they learn about time signatures and
reading music.

What is Meter?

The meter of a piece of music is the arrangment of its rhythms in a
repetitive pattern of strong and weak beats. This does not necessarily mean
that the rhythms themselves are repetitive, but they do strongly suggest a
repeated pattern of pulses. It is on these pulses, the beat of the music, that
you tap your foot, clap your hands, dance, etc.

Some music does not have a meter. Ancient music, such as Gregorian
chants; new music, such as some experimental twentieth-century art music;
and Non-Western music, such as some native American flute music, may
not have a strong, repetitive pattern of beats. Other types of music, such as
traditional Western African drumming, may have very complex meters that
can be difficult for the beginner to identify.

But most Western music has simple, repetitive patterns of beats. This makes
meter a very useful way to organize the music. Common notation, for
example, divides the written music into small groups of beats called
measures, or bars. The lines dividing each measure from the next help the
musician reading the music to keep track of the rhythms. A piece (or
section of the piece) is assigned a time signature that tells the performer
how many beats to expect in each measure, and what type of note should
get one beat. (For more on reading time signatures, please see Time
Signature.)

Conducting also depends on the meter of the piece; conductors use different
conducting patterns for the different meters. These patterns emphasize the
differences between the stronger and weaker beats to help the performers
keep track of where they are in the music.

But the conducting patterns depend only on the pattern of strong and weak
beats. In other words, they only depend on "how many beats there are in a
measure", not "what type of note gets a beat". So even though the time
signature is often called the "meter" of a piece, one can talk about meter
without worrying about the time signature or even being able to read music.
(Teachers, note that this means that children can be introduced to the
concept of meter long before they are reading music. See Meter Activities
for some suggestions. )

Classifying Meters

Meters can be classified by counting the number of beats from one strong
beat to the next. For example, if the meter of the music feels like "strong-
weak-strong-weak", it is in duple meter. "strong-weak-weak-strong-weak-
weak" is triple meter, and "strong-weak-weak-weak" is quadruple. (Most
people don't bother classifying the more unusual meters, such as those with
five beats in a measure.)

Meters can also be classified as either simple or compound. In a simple
meter, each beat is basically divided into halves. In compound meters, each
beat is divided into thirds.

A borrowed division occurs whenever the basic meter of a piece is
interrupted by some beats that sound like they are "borrowed" from a
different meter. One of the most common examples of this is the use of
triplets to add some compound meter to a piece that is mostly in a simple
meter. (See Dots, Ties, and Borrowed Divisions to see what borrowed
divisions look like in common notation.)

Recognizing Meters

To learn to recognize meter, remember that (in most Western music) the
beats and the subdivisions of beats are all equal and even. So you are
basically listening for a running, even pulse underlying the rhythms of the
music. For example, if it makes sense to count along with the music "ONE-
and-Two-and-ONE-and-Two-and" (with all the syllables very evenly
spaced) then you probably have a simple duple meter. But if it's more

comfortable to count "ONE-and-a-Two-and-a-ONE-and-a-Two-and-a", it's
probably compound duple meter. (Make sure numbers always come on a
pulse, and "one" always on the strongest pulse.)

This may take some practice if you're not used to it, but it can be useful
practice for anyone who is learning about music. To help you get started,
the figure below sums up the most-used meters. To help give you an idea of
what each meter should feel like, here are some animations (with sound) of
duple simple, duple compound, triple simple, triple compound, quadruple
simple, and quadruple compound meters. You may also want to listen to
some examples of music that is in simple duple, simple triple, simple

Meters
Meter Count Example Time Signature

Remember that meter is not the same as time
signature; the time signatures given here are just
examples. For example, 2/2 and 2/8 are also simple
duple meters.

Introduction to Subdivisions in Compound Meters
Introduction to subdivisions in compound meters. This module follows
Rhythmic Study: Introduction to Subdivisions in Simple Meters (m22810).

Introduction to Subdivisions in Compound Meters

Subdivisions in compound meters (6/8, 9/8, 12/8 etc.) generally feature
divisions of three eighth notes to each beat or pulse. Naturally each eighth
note may then be divided with sixteenth notes:

First perform the following by tapping eighth notes while singing the
melody with “Ta” or “La” or playing it on your instrument.

Once you have mastered that exercise, try to “hear” the tapping internally.
Play the upper line while hearing the tapping.

Try this example in 6/8 with sixteenth note subdivisions:

A good rule of thumb is to subdivide with the smallest note value possible.
If the example above was performed at a slow tempo, eighth note = 60, then
subdivisions with 32"¢ notes would be quite possible and would help to
ensure proper note values. At a tempo of dotted quarter note = 100,
sixteenth note subdivisions would be preferred. This new tempo would be
too rapid to subdivide easily with 32"¢ notes.

Here are some further examples to subdivide with sixteenth notes (Wedge,
p. 165):

SJR Td id. ooded 3
Bd: dd d. ee eee
ere ra ere

Pickup Notes and Measures

A shortened first measure of a piece of music is called a pickup measure.
Notes that begin a phrase shortly before a strong downbeat are also called
pickup notes.

Pickup Measures

Normally, all the measures of a piece of music must have exactly the
number of beats indicated in the time signature. The beats may be filled
with any combination of notes or rests (with duration values also dictated
by the time signature), but they must combine to make exactly the right
number of beats. If a measure or group of measures has more or fewer
beats, the time signature must change.

Normally, a composer who wants to put more or
fewer beats in a measure must change the time
signature, as in this example from Mussorgsky's
Boris Godunov.

There is one common exception to this rule. (There are also some less
common exceptions not discussed here.) Often, a piece of music does not
begin on the strongest downbeat. Instead, the strong beat that people like to
count as "one" (the beginning of a measure), happens on the second or third
note, or even later. In this case, the first measure may be a full measure that
begins with some rests. But often the first measure is simply not a full
measure. This shortened first measure is called a pickup measure.

If there is a pickup measure, the final measure of the piece should be
shortened by the length of the pickup measure (although this rule is

sometimes ignored in less formal written music). For example, if the meter
of the piece has four beats, and the pickup measure has one beat, then the
final measure should have only three beats. (Of course, any combination of
notes and rests can be used, as long as the total in the first and final
measures equals one full measure.

If a piece begins with a pickup measure, the final
measure of the piece is shortened by the length of the
pickup measure.

Pickup Notes

Any phrase of music (not just the first one) may begin someplace other than
on a strong downbeat. All the notes before the first strong downbeat of any
phrase are the pickup notes to that phrase.

Phrase 1 Phrase 2

Any phrase may begin with pickup notes. Each of these

four phrases begins with one or two pickup notes. (You

may listen to the tune here; can you hear that the pickup
notes lead to the stronger downbeat?)

A piece that is using pickup measures or pickup notes may also sometimes
place a double bar (with or without repeat signs) inside a measure, in order
to make it clear which phrase and which section of the music the pickup
notes belong to. If this happens (which is a bit rare, because it can be
confusing to read), there is still a single bar line where it should be, at the
end of the measure.

e ===

At the ends of sections of the music, a measure may be

interrupted by a double bar that places the pickup notes

in the correct section and assures that repeats have the
correct number of beats. When this happens, the bar

line will still appear at the end of the completed

measure. This notation can be confusing, though, and in

some music the pickups and repeats are written in a
way that avoids these broken-up measures.

Tempo
An introduction to the basic element of music called tempo, with some
useful terms.

The tempo of a piece of music is its speed. There are two ways to specify a
tempo. Metronome markings are absolute and specific. Other tempo
markings are verbal descriptions which are more relative and subjective.
Both types of markings usually appear above the staff, at the beginning of
the piece, and then at any spot where the tempo changes. Markings that ask
the player to deviate slightly from the main tempo, such as ritardando may
appear either above or below the staff.

Metronome Markings

Metronome markings are given in beats per minute. They can be estimated
using a clock with a second hand, but the easiest way to find them is with a
metronome, which is a tool that can give a beat-per-minute tempo as a
clicking sound or a pulse of light. [link] shows some examples of
metronome markings.

o = 88
Four four time
(quarter note gets one beat)
~ 88 beats, or 88 quarter notes, per minute
2=120
Cut time (two two)
(half note gets one beat)
e 120 beats, or 120 half notes, per minute
J. = 80 Six eight time
Probably dotted quarter gets one beat
80 dotted quarters per minute
e {This would be the same speed as ) = 240 .)
= a Six eight time

148 eighth notes per minute
Could be conducted in a fast six (eighth note gets one beat)
e or in a slow two (dotted quarter gets one beat: about @:=50 }

Metronomes often come with other tempo indications written on them, but
this is misleading. For example, a metronome may have allegro marked at
120 beats per minute and andante marked at 80 beats per minute. Allegro
should certainly be quite a bit faster than andante, but it may not be exactly
120 beats per minute.

Tempo Terms

A tempo marking that is a word or phrase gives you the composer's idea of
how fast the music should feel. How fast a piece of music feels depends
on several different things, including the texture and complexity of the
music, how often the beat gets divided into faster notes, and how fast the
beats themselves are (the metronome marking). Also, the same tempo
marking can mean quite different things to different composers; if a
metronome marking is not available, the performer should use a knowledge
of the music's style and genre, and musical common sense, to decide on the
proper tempo. When possible, listening to a professional play the piece can
help with tempo decisions, but it is also reasonable for different performers
to prefer slightly different tempos for the same piece.

Traditionally, tempo instructions are given in Italian.
Some Common Tempo Markings

e Grave - very slow and solemn (pronounced "GRAH-vay")
e Largo - slow and broad ("LAR-go")

e Larghetto - not quite as slow as largo ("lar-GET-oh")

e Adagio - slow ("uh-DAH-jee-oh")

e Lento - slow ("LEN-toe")

e Andante - literally "walking", a medium slow tempo ("on-DON-tay")
e Moderato - moderate, or medium ("MOD-er-AH-toe")

e Allegretto - Not as fast as allegro ("AL-luh-GRET-oh")

e Allegro - fast (“uh-LAY-grow")

e Vivo, or Vivace - lively and brisk (""VEE-voh")

e Presto - very fast ("PRESS-toe")

e Prestissimo - very, very fast ("press-TEE-see-moe")

These terms, along with a little more Italian, will help you decipher most
tempo instructions.
More useful Italian

¢ (un) poco - a little ("oon POH-koe")

¢ molto - a lot ("MOLE-toe")

¢ piu - more ("pew")

e meno - less ("MAY-no"

e mosso - literally "Moved"; motion or movement ("MOE-so")

Exercise:

Problem:

Check to see how comfortable you are with Italian tempo markings by
translating the following.

1. un poco allegro

2. molto meno mosso
3. piu vivo

4. molto adagio

5. poco piu mosso

Solution:

1. a little fast

2. much less motion = much slower
3. more lively = faster

4. very slow

5. a little more motion = a little faster

Of course, tempo instructions don't have to be given in Italian. Much folk,
popular, and modern music, gives instructions in English or in the
composer's language. Tempo indications such as "Not too fast", "With
energy", "Calmly", or "March tempo" give a good idea of how fast the
music should feel.

Gradual Tempo Changes

If the tempo of a piece of music suddenly changes into a completely
different tempo, there will be a new tempo given, usually marked in the
Same way (metronome tempo, Italian term, etc.) as the original tempo.
Gradual changes in the basic tempo are also common in music, though, and
these have their own set of terms. These terms often appear below the staff,
although writing them above the staff is also allowed. These terms can also
appear with modifiers like molto or un poco. You may notice that there are
quite a few terms for slowing down. Again, the use of these terms will vary
from one composer to the next; unless beginning and ending tempo
markings are included, the performer must simply use good musical
judgement to decide how much to slow down in a particular ritardando or
rallentando.

Gradual Tempo Changes

e accelerando - (abbreviated accel.) accelerating; getting faster

e ritardando - (abbrev. rit.) slowing down

e ritenuto - (abbrev. riten.) slower

e rallentando - (abbrev. rall.) gradually slower

e rubato - don't be too strict with the rhythm; while keeping the basic
tempo, allow the music to gently speed up and relax in ways that
emphasize the phrasing

¢ poco a poco - little by little; gradually

e¢ Tempo I - ("tempo one" or "tempo primo") back to the original tempo
(this instruction usually appears above the staff)